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MathsAges 16-18

Polygon interior angle sums

Use (n − 2) × 180° to calculate the sum of interior angles of an n-sided polygon. Review suitability for your learners before teaching.

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Age band:Ages 13-15Ages 16-18

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Worksheet StudioPractice pack · Ages 16-18

Polygon interior angle sums

Take your time. Show your thinking.

  1. 1. Calculate the sum of the interior angles of a 26-sided polygon using (n − 2) × 180°.

    26 · 2 · 180° · Polygon interior angle sums

  2. 2. Calculate the sum of the interior angles of a 3-sided polygon using (n − 2) × 180°.

    3 · 2 · 180° · Polygon interior angle sums

  3. 3. Calculate the sum of the interior angles of a 5-sided polygon using (n − 2) × 180°.

    5 · 2 · 180° · Polygon interior angle sums

  4. 4. Calculate the sum of the interior angles of a 9-sided polygon using (n − 2) × 180°.

    9 · 2 · 180° · Polygon interior angle sums

  5. 5. Calculate the sum of the interior angles of a 24-sided polygon using (n − 2) × 180°.

    24 · 2 · 180° · Polygon interior angle sums

  6. 6. Calculate the sum of the interior angles of a 22-sided polygon using (n − 2) × 180°.

    22 · 2 · 180° · Polygon interior angle sums

  7. 7. Calculate the sum of the interior angles of a 17-sided polygon using (n − 2) × 180°.

    17 · 2 · 180° · Polygon interior angle sums

  8. 8. Calculate the sum of the interior angles of a 15-sided polygon using (n − 2) × 180°.

    15 · 2 · 180° · Polygon interior angle sums

  9. 9. Calculate the sum of the interior angles of a 20-sided polygon using (n − 2) × 180°.

    20 · 2 · 180° · Polygon interior angle sums

  10. 10. Calculate the sum of the interior angles of a 11-sided polygon using (n − 2) × 180°.

    11 · 2 · 180° · Polygon interior angle sums

  11. 11. Calculate the sum of the interior angles of a 12-sided polygon using (n − 2) × 180°.

    12 · 2 · 180° · Polygon interior angle sums

  12. 12. Calculate the sum of the interior angles of a 25-sided polygon using (n − 2) × 180°.

    25 · 2 · 180° · Polygon interior angle sums
12 questions · Seed 49 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 16-18

Polygon interior angle sums

Answers and reasoning. Review before teaching.

  1. 1. Calculate the sum of the interior angles of a 26-sided polygon using (n − 2) × 180°.

    4320°

    Substitute n = 26: (26 − 2) × 180° = 24 × 180° = 4320°.

  2. 2. Calculate the sum of the interior angles of a 3-sided polygon using (n − 2) × 180°.

    180°

    Substitute n = 3: (3 − 2) × 180° = 1 × 180° = 180°.

  3. 3. Calculate the sum of the interior angles of a 5-sided polygon using (n − 2) × 180°.

    540°

    Substitute n = 5: (5 − 2) × 180° = 3 × 180° = 540°.

  4. 4. Calculate the sum of the interior angles of a 9-sided polygon using (n − 2) × 180°.

    1260°

    Substitute n = 9: (9 − 2) × 180° = 7 × 180° = 1260°.

  5. 5. Calculate the sum of the interior angles of a 24-sided polygon using (n − 2) × 180°.

    3960°

    Substitute n = 24: (24 − 2) × 180° = 22 × 180° = 3960°.

  6. 6. Calculate the sum of the interior angles of a 22-sided polygon using (n − 2) × 180°.

    3600°

    Substitute n = 22: (22 − 2) × 180° = 20 × 180° = 3600°.

  7. 7. Calculate the sum of the interior angles of a 17-sided polygon using (n − 2) × 180°.

    2700°

    Substitute n = 17: (17 − 2) × 180° = 15 × 180° = 2700°.

  8. 8. Calculate the sum of the interior angles of a 15-sided polygon using (n − 2) × 180°.

    2340°

    Substitute n = 15: (15 − 2) × 180° = 13 × 180° = 2340°.

  9. 9. Calculate the sum of the interior angles of a 20-sided polygon using (n − 2) × 180°.

    3240°

    Substitute n = 20: (20 − 2) × 180° = 18 × 180° = 3240°.

  10. 10. Calculate the sum of the interior angles of a 11-sided polygon using (n − 2) × 180°.

    1620°

    Substitute n = 11: (11 − 2) × 180° = 9 × 180° = 1620°.

  11. 11. Calculate the sum of the interior angles of a 12-sided polygon using (n − 2) × 180°.

    1800°

    Substitute n = 12: (12 − 2) × 180° = 10 × 180° = 1800°.

  12. 12. Calculate the sum of the interior angles of a 25-sided polygon using (n − 2) × 180°.

    4140°

    Substitute n = 25: (25 − 2) × 180° = 23 × 180° = 4140°.

12 questions · Seed 49 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Polygon interior angle sums

Take your time. Show your thinking.

  1. 1. Calculate the sum of the interior angles of a 26-sided polygon using (n − 2) × 180°.

    26 · 2 · 180° · Polygon interior angle sums

  2. 2. Calculate the sum of the interior angles of a 3-sided polygon using (n − 2) × 180°.

    3 · 2 · 180° · Polygon interior angle sums

  3. 3. Calculate the sum of the interior angles of a 5-sided polygon using (n − 2) × 180°.

    5 · 2 · 180° · Polygon interior angle sums

  4. 4. Calculate the sum of the interior angles of a 9-sided polygon using (n − 2) × 180°.

    9 · 2 · 180° · Polygon interior angle sums

  5. 5. Calculate the sum of the interior angles of a 24-sided polygon using (n − 2) × 180°.

    24 · 2 · 180° · Polygon interior angle sums

  6. 6. Calculate the sum of the interior angles of a 22-sided polygon using (n − 2) × 180°.

    22 · 2 · 180° · Polygon interior angle sums

  7. 7. Calculate the sum of the interior angles of a 17-sided polygon using (n − 2) × 180°.

    17 · 2 · 180° · Polygon interior angle sums

  8. 8. Calculate the sum of the interior angles of a 15-sided polygon using (n − 2) × 180°.

    15 · 2 · 180° · Polygon interior angle sums

  9. 9. Calculate the sum of the interior angles of a 20-sided polygon using (n − 2) × 180°.

    20 · 2 · 180° · Polygon interior angle sums

  10. 10. Calculate the sum of the interior angles of a 11-sided polygon using (n − 2) × 180°.

    11 · 2 · 180° · Polygon interior angle sums

  11. 11. Calculate the sum of the interior angles of a 12-sided polygon using (n − 2) × 180°.

    12 · 2 · 180° · Polygon interior angle sums

  12. 12. Calculate the sum of the interior angles of a 25-sided polygon using (n − 2) × 180°.

    25 · 2 · 180° · Polygon interior angle sums
12 questions · Seed 49 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Polygon interior angle sums

Answers and reasoning. Review before teaching.

  1. 1. Calculate the sum of the interior angles of a 26-sided polygon using (n − 2) × 180°.

    4320°

    Substitute n = 26: (26 − 2) × 180° = 24 × 180° = 4320°.

  2. 2. Calculate the sum of the interior angles of a 3-sided polygon using (n − 2) × 180°.

    180°

    Substitute n = 3: (3 − 2) × 180° = 1 × 180° = 180°.

  3. 3. Calculate the sum of the interior angles of a 5-sided polygon using (n − 2) × 180°.

    540°

    Substitute n = 5: (5 − 2) × 180° = 3 × 180° = 540°.

  4. 4. Calculate the sum of the interior angles of a 9-sided polygon using (n − 2) × 180°.

    1260°

    Substitute n = 9: (9 − 2) × 180° = 7 × 180° = 1260°.

  5. 5. Calculate the sum of the interior angles of a 24-sided polygon using (n − 2) × 180°.

    3960°

    Substitute n = 24: (24 − 2) × 180° = 22 × 180° = 3960°.

  6. 6. Calculate the sum of the interior angles of a 22-sided polygon using (n − 2) × 180°.

    3600°

    Substitute n = 22: (22 − 2) × 180° = 20 × 180° = 3600°.

  7. 7. Calculate the sum of the interior angles of a 17-sided polygon using (n − 2) × 180°.

    2700°

    Substitute n = 17: (17 − 2) × 180° = 15 × 180° = 2700°.

  8. 8. Calculate the sum of the interior angles of a 15-sided polygon using (n − 2) × 180°.

    2340°

    Substitute n = 15: (15 − 2) × 180° = 13 × 180° = 2340°.

  9. 9. Calculate the sum of the interior angles of a 20-sided polygon using (n − 2) × 180°.

    3240°

    Substitute n = 20: (20 − 2) × 180° = 18 × 180° = 3240°.

  10. 10. Calculate the sum of the interior angles of a 11-sided polygon using (n − 2) × 180°.

    1620°

    Substitute n = 11: (11 − 2) × 180° = 9 × 180° = 1620°.

  11. 11. Calculate the sum of the interior angles of a 12-sided polygon using (n − 2) × 180°.

    1800°

    Substitute n = 12: (12 − 2) × 180° = 10 × 180° = 1800°.

  12. 12. Calculate the sum of the interior angles of a 25-sided polygon using (n − 2) × 180°.

    4140°

    Substitute n = 25: (25 − 2) × 180° = 23 × 180° = 4140°.

12 questions · Seed 49 · Age guidance, not curriculum certification